High performance computing for partial differential equations

When representing realistic physical phenomena by partial differential equations (PDE), it is crucial to approximate the underlying physics correctly, to get precise results, and to efficiently use the computer architecture. Incorrect results can appear in incompressible Navier–Stokes or Stokes problems when the numerical approach couples into spurious modes. In Maxwell or magnetohydrodynamic (MHD) equations the so-called spectrum pollution effect can occur, and the numerical solution does not stably converge to the physical one. Problems coming from a mesh that is not adapted to the underlying physical problem, or from an inadequate choice of the dependent and independent variables can lead to low precision. Efficiency of a code implementation can be improved by well adapting the parallel computer to the application. A new monitoring system enables to detect poor implementations, to find best suited resources to execute the job, and to adapt the processor frequency during.